Question

Given f(x) and g(x) = kf(x), use the graph to determine the value of k.

Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 3, 1. Line g of x passes through points negative 4, 0 and negative 3, negative 2.

−2
negative one half
one half
2

Answer 1

k = -2

Explanation:

From the given information, we understand that f(x) and g(x) are linear functions and that g(x) takes the output of f(x)—its y-value—and multiplies it by a constant k to form its output.

So, we can solve for k by finding the proportion between the output, or y-coordinate, of g(x) at a certain x-value, and output of f(x) at the same x-value.

We are given the following points:

• (-3, 1) for f(x)
• (-3, -2) for g(x)

We can divide the y-coord. of g(x) by the y-coord. of f(x) at the same x-value (which happens to be -3) to solve for the proportion, which is k.

k = -2 / 1

k = -2